Acceleration of a box pulled up a ramp with friction

In summary, a 160kg box on a 35 degree incline plane with a tension of 1240 N attached to a pulley will not move up the ramp due to the force of friction being greater than the tension. The force of static friction, gravity down the ramp, and total force on the box were calculated to support this conclusion.
  • #1
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Homework Statement


A 160kg box is on a plane with an incline of 35 degrees. A rope is attached to the box and a pulley at the top of the ramp and has a tension of 1240 N. The static coefficient of friction is 0.45. Will the box move up the ramp? If so, what is its acceleration?

Homework Equations


Total force on box = m*a
Is Force of tension >= Force of friction + Force of gravity down ramp(?)

Force of static friction = umg*cos(theta) = 0.45*160.0*9.81*cos(35) = 579 N
Force of gravity down ramp = mg*sin(theta) = 160.0*9.81*sin(35) = 900 N

The Attempt at a Solution


Force Total = m * a
1240 N >= 579 N - 900 N
1240 N >= 1479 N -> No it won't slide up the ramp.

I hope this is correct, I'm not sure if using the force acting down the ramp is correct or not.
 
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  • #2
Well done, it looks good to me.
 
  • #3
The next problem implies the box reaches the top of the ramp and we are given a coefficient of kinetic friction, So I want to make extra sure.
 
  • #4
I just read over it again and it looks fine.
 

FAQ: Acceleration of a box pulled up a ramp with friction

1. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a measure of how quickly an object's speed or direction is changing.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in an object's velocity by the time it takes for that change to occur. The formula for acceleration is a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. How does friction affect the acceleration of a box pulled up a ramp?

Friction is a force that opposes motion, so it will act in the opposite direction of the box's movement up the ramp. This means that friction will decrease the acceleration of the box, making it move slower than it would without friction.

4. What factors can affect the acceleration of a box pulled up a ramp with friction?

The factors that can affect the acceleration of a box pulled up a ramp with friction include the amount of friction present, the angle of the ramp, the mass of the box, and the force applied to pull the box up the ramp. Other factors such as air resistance and surface conditions may also play a role.

5. How can the acceleration of a box pulled up a ramp with friction be increased?

The acceleration of a box pulled up a ramp with friction can be increased by decreasing the amount of friction present, increasing the angle of the ramp, decreasing the mass of the box, or increasing the force applied to pull the box up the ramp. Additionally, using a smoother surface or reducing air resistance can also help increase acceleration.

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